April | 2009 | Annoying Precision

Archive for April, 2009

The spectral radius of a simple graph

Posted in math.CO, tagged walks on graphs on April 30, 2009| 3 Comments »

I’ve decided not to port over the posts from AoPS. Among other things, I’d prefer to preserve the comments on older posts as they are.

So here’s something I’ve been thinking about. Given a simple connected graph $G$ , define $\rho(G)$ to be its largest positive eigenvalue; in other words, if $w_n$ counts the number of walks (equivalently, closed walks) of length $n$ on $G$ , then

$\displaystyle \rho(G) = \limsup_{n \to \infty} \sqrt[n]{w_n}.$

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Annoying Precision

"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." – Paul Halmos

Archive for April, 2009

The spectral radius of a simple graph

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